I have a Boss NS2 Noise Suppressor that I leave on all the time, if that counts--all my "gain" pedals are in its noise-reduction loop, and it could be very noisy with single-coils without it.
As far as pedals that add something rather than removing it, my Digitech DigiVerb, set to a low level, is on whenever I'm running an amp w/o onboard reverb. I like a little "space" in my tone.
I also usually have my BYOC analog delay on, too, set to a short interval and not much regen, just to fill out the sound some. If I kick in another modulation effect (phaser, flanger, chorus, trem), the delay goes back off, or it just gets too "busy"....